Assume you are choosing between two goods, X and Y, and your total utility from each is as shown below.

Quantity

TUx

MUx/P_X=$2

TUy

MUy/P_y=$1

MU_X/P_x=$1

0

0

0

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1

10

8

2

18

15

3

24

21

4

28

26

5

31

30

6

33

33

(a)If your income is $9 and the prices of X and Y are $2 and $1 respectively, what quantities of each good will you purchase in maximizing your utility?What is the amount of total utility?Are the conditions for utility maximization satisfied? Explain (20 points)

(b)Assume that, other things remaining unchanged, the price of X falls from $2 to $1.What quantities of X and Y will you now purchase?What is the amount of total utility now? (10 points)

(c) Given the change in the price of good X in section (b), explain why the law of demand holds. (10 points)